Effects of Early Warning Emails on Student Performance

class: title-slide

<br>
<br>
# Effects of Early Warning Emails on Student Performance <br>

.padding_left.pull-down.white[
.bold[_J. Klenke_], T. Massing, N. Reckmann, J. Langerbein, B. Otto, M. Goedicke, C. Hanck
<br>
<br>
<br>
`$15^{TH}$` International Conference on Computer Supported Education

Prague, 21-23 April, 2023
]

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# Outline

<br>

1. [Research Idea and Course Description](#course)
1. [Literature on Warning Systems in Education](#literature)
1. [Used Model: Rregression Discounity Design](#RDD)
1. [Empirical Results](#results)
1. [Discussion](#discussion)
1. [Further Research](#f_reaserach)
1. [Appendix](#appendix)
1. [References](#references)

---
name: course
# Research Idea and Course Description

- __Research Idea:__ students should receive objective and motivating feedback through a warning email   
- Analyzed Course: _Inferential Statistics_ at the University of Duisburg-Essen of the summer semester 2019
- Compulsory course for several business and economics programs
  - Weekly 2-hour lecture 
  - Weekly 2-hour exercise
  - [Kahoot!](https://kahoot.com/) games were used to interact with students during classes
  - Homework and 5 online tests were offered on the e-assessment platform  [JACK](https://s3.paluno.uni-due.de/en/forschung/spalte1/e-learning-und-e-assessment)
- Over all systems we gathered information of __802__ individuals 
  - __337__ students took an exam at the end of the semester

---
# Data and Decision Rule

<br>
- We used two data sources 
  - First three online test results  
  - Cumulative points of the tasks in JACK
- Logit model was used to predict students probability to pass the exam based on the first 3 online tests
  - Model was trained with the latest data obtained from previous edition of the same course
- If predicted probability to pass `$\leq 0.4$` the student got a warning mail

---
# Course Timeline Main Events

<br>

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#plots/timeline_plot.png" alt="Timeline for the key events in the 2019 summer term course Inferential Statistics (treatment cohort)." width="80%" />
<p class="caption">Timeline for the key events in the 2019 summer term course Inferential Statistics (treatment cohort).</p>
</div>

- The shaded area indicates the period after treatment. 
- 57 days between the warning mail and `$1^{st}$` exam 
- 113 days between the warning email and `$2^{nd}$` exam

---
name: literature
# Literature on Warning Systems in Education

.font80[
- <a id='cite-Arnold2012'></a><a href='#bib-Arnold2012'>Arnold and Pistilli (2012)</a> investigated the effect of the signal light system at the Purdue University and found a positive effect on student grades
- <a id='cite-baneres2020'></a><a href='#bib-baneres2020'>Bañeres, Rodríguez, Guerrero-Roldán, and Karadeniz (2020)</a> implemented an early warning system but did not analysed the effect on students' performance
- <a id='cite-csahin2019'></a><a href='#bib-csahin2019'>Şahin and Yurdugül (2019)</a> invented an _Intelligent Intervention System_ where for each assessment the students get feedback. Students emphasized the usefulness of the system. 
- <a id='cite-Iver2019'></a><a href='#bib-Iver2019'>Mac Iver, Stein, Davis, Balfanz, and Fox (2019)</a> could not find an effect from their early waning system in the ninth grad.
- <a id='cite-Edmunds2002'></a><a href='#bib-Edmunds2002'>Edmunds and Tancock (2002)</a> analyzed the effects of incentives on third and four-graders' reading motivation and did not find an effect.  
]

--
<br>
.blockquote[
- The literature on the effects of warning system is inconclusive
- Many studies analyzed the sytstem with questionnaires

.padding_left_2[<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#004c93;" xmlns="http://www.w3.org/2000/svg">  <path d="M256 8c137 0 248 111 248 248S393 504 256 504 8 393 8 256 119 8 256 8zm-28.9 143.6l75.5 72.4H120c-13.3 0-24 10.7-24 24v16c0 13.3 10.7 24 24 24h182.6l-75.5 72.4c-9.7 9.3-9.9 24.8-.4 34.3l11 10.9c9.4 9.4 24.6 9.4 33.9 0L404.3 273c9.4-9.4 9.4-24.6 0-33.9L271.6 106.3c-9.4-9.4-24.6-9.4-33.9 0l-11 10.9c-9.5 9.6-9.3 25.1.4 34.4z"></path></svg> We try to measure the effect directly on students' performance]

]

---
name: RDD
# RDD Example &#8212; I

## Parametric Estimation

<br>

---
# RDD Example &#8212; II

## Non-parametric Estimation

- We used the data-driven approach by <a id='cite-imbensoptimal2009'></a><a href='#bib-imbensoptimal2009'>Imbens and Kalyanaraman (2009)</a> to determine the bandwidth

???
- The method fits the bandwidth as widely as possible without introducing other confounding effects

---
# Model Assumptions

- The running variable `$W$` (predicted probability to pass the exam) needs to be continuous around the cutoff, otherwise students could manipulate the treatment

.pull-left-2[
<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#plots/test_cont_label.png" alt="Graphical illustration of the McCrary sorting test." width="80%" />
<p class="caption">Graphical illustration of the McCrary sorting test.</p>
</div>
]

.pull-right-1[
<br>

- There is no jump in the density around the cutoff point of `$0.4$`. 
- `$p$`-value: `$0.509$`
- The incentive to manipulate the treatment is quiet low.

]

.pull-down[
- Also standard IV estimation assumptions must hold
]

---
name: results
# Empirical Results &#8212; I

.pull-left-2[

<br>
<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#plots/model_plot_label.png" alt="Graphical illustration of the RDD model." width="80%" />
<p class="caption">Graphical illustration of the RDD model.</p>
</div>
]

.pull-right-1[
### Estimates
- LATE: 0.193 (4.889)
- Bandwidth: 0.255
- `$F$`-statics: 0.257
- `$N$`: 126

<br>
- We also estimated the RDD with covariates 
  - The results were identical
]

???

- theoretisch sollten Sie jetzt einen großen Sprung sehen
---
# Empirical Results &#8212; II

- The LATE estimate is positive but not significant  
  - An estimate of `$0.193$` means that students who received the warning email achieved `$0.193$` points more than comparable students who did not 
  - Compared to the `$60$`-point exam, the effect size seems limited

- The bandwidth of `$0.255$` was determined with the data-driven approach of <a href='#bib-imbensoptimal2009'>Imbens and Kalyanaraman (2009)</a>.
  - Only students with a predicted probability `$0.4$` (cutoff) `$\pm 0.255$` (bandwidth), are included in the analysis.
  
--

- This leads to the sample size of `$126$` students.

---
name: discussion
# Discussion &#8212; I

- Our RDD results do not provide evidence that the warning email has a significant effect on students’ results (or behavior)
- The variance around the cutoff is rather high, which compromises the detection of an effect 
- Many individuals are not included in the final analysis for several reasons
  - Students dropping the course
  - Students far away from the cutoff are not providing much information for the model

.padding_left_2[<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#004c93;" xmlns="http://www.w3.org/2000/svg">  <path d="M256 8c137 0 248 111 248 248S393 504 256 504 8 393 8 256 119 8 256 8zm-28.9 143.6l75.5 72.4H120c-13.3 0-24 10.7-24 24v16c0 13.3 10.7 24 24 24h182.6l-75.5 72.4c-9.7 9.3-9.9 24.8-.4 34.3l11 10.9c9.4 9.4 24.6 9.4 33.9 0L404.3 273c9.4-9.4 9.4-24.6 0-33.9L271.6 106.3c-9.4-9.4-24.6-9.4-33.9 0l-11 10.9c-9.5 9.6-9.3 25.1.4 34.4z"></path></svg>  Thus precise estimation of the treatment becomes more difficult]

---
# Discussion &#8212; II

- Students get also feedback through their online tests
- The warning may also lead weak students to postpone participation to a later semester
  - The cost to postone exams are in our program quiet low
- The objective feedback and motivation from one warning email is rather small

---
name: f_reaserach
# Further Research

- The effect on the dropout rate from such warning emails or systems requires further attention 
- An automatic repeatedly feedback system could possibly have a greater impact on students motivation
  - A detailed recurring feedback could also used to guide students

<br>
.blockquote[
We see the open and transparent communication of the student’s performance to the students as a positive aspect of the system.
]

---
class: appendix eg
name: appendix
## Appendix: Regression Discontinuity Design (RDD)  &#8212; I

- The treatment is __not__ randomly assigned and therefore methods like OLS are not suitable
  - Treatment is a function of the predicted probability to pass the exam   
- Consider the following __sharp__ RDD representation <a id='cite-Huntington-Klein2022'></a><a href='#bib-Huntington-Klein2022'>Huntington-Klein (2022)</a>:

`$$Y_i = \beta_0 + \alpha T_i + \beta W_i + u_i$$`
.padding_left.padding_left.font80[
<ul>
  <li> $W_i$ denotes the predicted probability to pass the final exam</li>
  <li> $T_i$ indicates if a student received a mail</li>
  <ul style="list-style-type: '&#8227;  ';"  >
    <li>$T_i = 1[W_i \leq c]$ , with $c = 0.4$ </li>
  </ul>
  <li>$\alpha$ denotes the treatment effect</li>
  <li>$u_i$ denotes the error term</li>
</ul>
]

---
class: appendix eg
## Appendix: Regression Discontinuity Design (RDD) &#8212; II
### Appendix: Fuzzy RDD

- __Fuzzy__ RDD allows to analyse a treatment in a setting where the two groups are not perfectly separated
  - Only the likelihood of receiving the treatment needs to _change_
- The effect is estimated through an instrumental variable estimation 
<a id='cite-angristidentification1996'></a><a href='#bib-angristidentification1996'>Angrist, Imbens, and Rubin (1996)</a> where in the first stage the `$\widehat{T}_i$` are estimated which then are inserted in the second stage

- First Stage: 
`$$T_i = \gamma_0 +\gamma_i Z_i + \gamma_2  W_i + \nu_i \qquad \quad$$`

- Second Stage: 
`$$Y_i  = \beta_0 + \alpha \widehat{T}_i + \delta_1 W_i + \beta X_i + u_i$$`

---
class: appendix eg
## Appendix: Regression Discontinuity Design (RDD)  &#8212; III

.font70[
<ul>
  <li>RDD compares the individuals around the cutoff to estimate the effect</li>
  <li><strong>Main Assumption:</strong> Individuals around the cutoff are compareable and only differ in the treatment assignment</li>
  <ul>
    <li>The estimate is called Local Average Treatment Effect (<strong>LATE</strong>) </li>
  </ul>
  <li>For both methods, sharp and fuzzy,the estimation can be either parametric or non-parametric</li>
  <ul>
    <li>Parametric estimation</li>
    <ul>
      <li>Uses the whole sample size but (many) more parameters</li>
      <li>Individuals away from the cutoff are less relevant for the estimation of the effect</li>
    </ul>
    <li>Non-parametric estimation</li>
    <ul>
      <li>Only <em>comparable</em> (near the cutoff) individuals are used for the analysis</li>
      <ul>
        <li>Decision whether to include an individual depends on the running variable $W$</li>
        <li>The groups are determined by the the data-driven approach of Imbens and Kalyanaraman (2009)</li>
        <ul>
          <li>With an $F$-test the bandwidth is determined</li>
          <li>$c \pm bandwidth$ are the two groups</li>
        </ul>
      </ul>
    </ul>
  </ul>
</ul>
]

---
name: references
# References

.font80[

Angrist, J. D., G. Imbens, and D. B. Rubin (1996). "Identification of
Causal Effects Using Instrumental Variables". In: _Journal of the
American Statistical Association_ 91.434. Publisher: Taylor & Francis,
pp. 444-455.

Arnold, K. E. and M. Pistilli (2012). "Course signals at Purdue: using
learning analytics to increase student success". Eng. In: _ACM
International Conference Proceeding Series_. LAK '12. ACM, pp. 267-270.

Bañeres, D., M. E. Rodríguez, A. E. Guerrero-Roldán, et al. (2020). "An
Early Warning System to Detect At-Risk Students in Online Higher
Education". In: _Applied Sciences_ 10.13, p. 4427.

Edmunds, K. and S. M. Tancock (2002). "Incentives: The effects on the
reading motivation of fourth‐grade students". In: _Reading Research and
Instruction_ 42.2, pp. 17-37.

Huntington-Klein, N. (2022). _The effect : an introduction to research
design and causality_. First edition.  Chapman & Hall book. Boca Raton
; London ; New York: CRC Press, Taylor & Francis Group.

Imbens, G. and K. Kalyanaraman (2009). "Optimal Bandwidth Choice for
the Regression Discontinuity Estimator". In: _National Bureau of
Economic Research_ 1.14726.

Mac Iver, M. A., M. L. Stein, M. H. Davis, et al. (2019). "An Efficacy
Study of a Ninth-Grade Early Warning Indicator Intervention". In:
_Journal of Research on Educational Effectiveness_ 12.3, pp. 363-390.

Şahin, M. and H. Yurdugül (2019). "An intervention engine design and
development based on learning analytics: the intelligent intervention
system (In 2 S)". In: _Smart Learning Environments_ 6.1, p. 18.
]